How do vector registers work in terms of calculations and alloting data to them ?
Is there a detailed reference available somewhere explaining how vector registers work and how data is fetched from them ?

Well, one of the earliest vector registers was the H/L register pair. I think that dates back to the 8080, perhaps the 8008. In the end, a vector register is nothing very special. Instructions still need to specify input register(s), output register(s), and operations. On a silicon level, it means that one operation is dispatched multiple times with different registers, usually in parallel.